Gas laws identification: “The absolute pressure of a fixed mass of a perfect gas varies inversely with its volume at constant temperature.” Does this statement describe Charles’ law?
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AYes
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BNo
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COnly at very low temperatures
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DOnly for monatomic gases
Answer
Correct Answer: No
Explanation
Introduction / Context:Several classical gas laws describe limiting relationships among p, V, and T. Correctly matching statements to their proper names avoids confusion in thermodynamics and fluid mechanics calculations.
Given Data / Assumptions:
- Ideal gas behavior.
- Temperature held constant (isothermal condition) in the statement.
- Fixed mass of gas.
Concept / Approach:The statement “pressure varies inversely with volume at constant temperature” is Boyle’s law, not Charles’ law. Charles’ law states that for a fixed mass at constant pressure, volume is directly proportional to absolute temperature (V ∝ T). Meanwhile, Gay-Lussac’s law states that at constant volume, pressure is proportional to temperature (p ∝ T). Recognizing which variable is held constant is the key to correct identification.
Step-by-Step Solution:
Identify condition: T constant ⇒ isothermal relation.Apply ideal gas law pV = nRT ⇒ with T constant, p ∝ 1/V → Boyle’s law.Therefore, the statement does not describe Charles’ law.Verification / Alternative check:Mnemonic: B (Boyle) links p and V; C (Charles) links V and T; G (Gay-Lussac) links p and T—each with the third variable constant.
Why Other Options Are Wrong:
- Yes: Mislabels Boyle’s law as Charles’ law.
- Other qualifiers: Temperature or gas type limitations are irrelevant to the naming.
Common Pitfalls:Swapping Boyle and Charles due to both being simple proportionality laws; forgetting which variable is constant in each statement.
Final Answer:No